Bilbao Crystallographic Server arrow Wyckoff Sets: Equivalent Sets of Wyckoff Positions

Wyckoff Sets of Space Group Pnnm (No. 58)

NOTE: The program uses the default choice for the group settings.

Letter Mult SS Rep. Equivalent WP under
Euclidean normalizer		 Equivalent WP under
affine normalizer
h 8 1 (x, y, z) h h
g 4 ..m (x, y, 0) g g
f 4 ..2 (0, 1/2 , z) ef ef
e 4 ..2 (0, 0, z) ef ef
d 2 ..2/m (0, 1/2 , 1/2 ) abcd abcd
c 2 ..2/m (0, 1/2 , 0) abcd abcd
b 2 ..2/m (0, 0, 1/2 ) abcd abcd
a 2 ..2/m (0, 0, 0) abcd abcd

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of Pnnm (058) under the coset representatives of its affine normalizer


Index: 16

No. # Coset Representative Transformed WP
1x,y,z
(
   1   0   0    0
   0   1   0    0
   0   0   1    0
)
 
a b c d e f g h
2x+1/2,y,z
(
   1   0   0   1/2
   0   1   0    0
   0   0   1    0
)
 
d c b a f e g h
3x,y+1/2,z
(
   1   0   0    0
   0   1   0   1/2
   0   0   1    0
)
 
c d a b f e g h
4x,y,z+1/2
(
   1   0   0    0
   0   1   0    0
   0   0   1   1/2
)
 
b a d c e f g h
5x+1/2,y+1/2,z
(
   1   0   0   1/2
   0   1   0   1/2
   0   0   1    0
)
 
b a d c e f g h
6x+1/2,y,z+1/2
(
   1   0   0   1/2
   0   1   0    0
   0   0   1   1/2
)
 
c d a b f e g h
7x,y+1/2,z+1/2
(
   1   0   0    0
   0   1   0   1/2
   0   0   1   1/2
)
 
d c b a f e g h
8x+1/2,y+1/2,z+1/2
(
   1   0   0   1/2
   0   1   0   1/2
   0   0   1   1/2
)
 
a b c d e f g h
9y,x,z
(
   0   1   0    0
   1   0   0    0
   0   0   1    0
)
 
a b d c e f g h
10y+1/2,x,z
(
   0   1   0   1/2
   1   0   0    0
   0   0   1    0
)
 
c d b a f e g h
11y,x+1/2,z
(
   0   1   0    0
   1   0   0   1/2
   0   0   1    0
)
 
d c a b f e g h
12y,x,z+1/2
(
   0   1   0    0
   1   0   0    0
   0   0   1   1/2
)
 
b a c d e f g h
13y+1/2,x+1/2,z
(
   0   1   0   1/2
   1   0   0   1/2
   0   0   1    0
)
 
b a c d e f g h
14y+1/2,x,z+1/2
(
   0   1   0   1/2
   1   0   0    0
   0   0   1   1/2
)
 
d c a b f e g h
15y,x+1/2,z+1/2
(
   0   1   0    0
   1   0   0   1/2
   0   0   1   1/2
)
 
c d b a f e g h
16y+1/2,x+1/2,z+1/2
(
   0   1   0   1/2
   1   0   0   1/2
   0   0   1   1/2
)
 
a b d c e f g h


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